Saturday, November 26, 2011

Fraction

Let's break the hexagon into 6 equal pieces:
whole hexagon and hexagon cut into 6 equal pieces
What if we just had one of the pieces?
one triangle of hexagon that's cut into 6 equal pieces
That would be 1 piece out of 6 pieces. Right?
Here's how we write it:
1/6 - the top number is called the numerator and the bottom number is called the denominator
We read this like "one sixth."
Let's do some more counting!

.....
How much of this hexagon is red?
hexagon cut into 6 equal triangles
5 pieces are red... out of 6 total pieces...
So, 5/6 of the hexagon is red.
How much is blue?
1 blue piece... out of 6...
1/6 of the hexagon is blue.

Saturday, November 12, 2011

Division

Let's see what's really going on when we divide one number into another number.
6/3=
We start with 6 triangles:
6 triangles
We want to see how many chunks of 3 we can make out of 6 things!
We can divide 6 things into 2 chunks of 3.
6 triangles split into two sets of three triangles
6/3=2

Now, let's see how many times 2 will go into 6.
6/2=
Start with 6 squares:
6 squares
We want to see how many chunks of 2 we can make out of 6 things!
We can divide 6 things into 3 chunks of 2.
6 squares spit into three sets of two squares
6/2=3

Multiplication

Let's see what's really going on when we multiply two numbers.
2x3=
This means that you have two groups of 3!
6 triangles split into 2 sets of 3 triangles
Put the two groups together...  How many triangles do you have?
6 triangles
Count them...  One, two, three, four, five, six!
So, our answer is:
2x3=6

Let's do another one!  This one has the numbers switched around.
3x2=
This means that you have three groups of 2!
6 squares split into 3 sets of 2 squares
Put the three groups together...  How many squares do you have?
6 squares
Count them...  One, two, three, four, five, six!
So, our answer is:
3x2=6
Hey, that's the same answer we got with 2 x 3!  But, we put the six together a different way.  Look at them both again to see the difference!

Subtraction (Two Digit Value)

For this lesson, we'll be working with easy numbers just to get you used to how this stuff works.
We're going to work with everything stacked because this is what you'll always do with bigger numbers.
We're going to work backwards, just like we did with addition! 
I'm going to have you subtract the ones first... then the tens.  Like addition, you'll have to do it this way when the numbers get harder.
Let's jump in!
89-32
Stack them and line everything up:
89-32
Subtract down the stripes...  Do the ones first, then the tens:
subtracting the ones for 89-32subtracting the tens for 89-32
So, 89-32=57